Heat Kernel and Analysis on Manifolds

Cover
Title page
Dedication
Contents
Preface
Laplace operator and the heat equation in ℝⁿ
Function spaces in ℝⁿ
Laplace operator on a Riemannian manifold
Laplace operator and heat equation in ?²(?)
Weak maximum principle and related topics
Regularity theory in ℝⁿ
The heat kernel on a manifold
Positive solutions
Heat kernel as a fundamental solution
Spectral properties
Distance function and completeness
Gaussian estimates in the integrated form
Green function and Green operator
Ultracontractive estimates and eigenvalues
Pointwise Gaussian estimates I
Pointwise Gaussian estimates II
Appendix A. Reference material
Bibliography
Some notation
Index
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